Piezoelectric, defined coupling coefficient

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

A filter is required to pass a certain selected frequency band, or to stop a given band. The passband for a piezoelectric device is proportional to k2, where k is the appropriate coupling coefficient. The very low k value of about 0.1 for quartz only allows it to pass frequency bands of approximately 1% of the resonant frequency. However, the PZT ceramics, with k values of typically about 0.5, can readily pass bands up to approximately 10% of the resonant frequency. Quartz has a very high Qm (about 106) which results in a sharp cut-off to the passband. This, coupled with its very narrow passband, is the reason why the frequency of quartz oscillators is very well defined. In contrast PZT ceramics have Qm values in the range 102—103 and so are unsuited to applications demanding tightly specified frequency characteristics. 

Choosing a thickness-polarized, thickness-vibrating piezoelectric element as an example, we can define the applied voltage V, current i, dimensions b, h, and /, and the output force and velocity F and the cross-sectional area bounded by b and / can be defined by A here it is assumed this area is electroded on the top and bottom faces of the element and that b and / are much greater than h. Treating it as a collection of discrete circuit elements as shown in Fig. lb, the Van Dyke circuit, allows the analysis of one resonance within the isolated element. Most piezoelectric materials are capacitive insulators, and the shunt capacitance Cs = bl/p h is the constant capacitance present across the element. The additional branch in the circuit represents the specific resonance being analyzed, the motional branch with inductance L, resistance R, and capacitance C. Many impedance analyzers provide this circuit as a means to model the electrical behavior of the piezoelectric element. The coupling coefficient for this... 

In the linearized theory with bias field of magnitude, a typical magnetoacoustic coupling coefficient (usually a small parameter) is defined by when and P2 are typical components of and This causes a lowering of the acoustic speed [9] while piezoelectricity expressed in terms of electric fields causes an increase in the acoustic speed [1]. It must also be noted that in a magnetic case one always has to solve interior and exterior problems matched by the boundary conditions (2.3)1 thus always expressed in terms of jumps, since there does... 

The piezoelectric effect entails a linear coupling between electrical and mechanical energies. Numerous piezoelectric coefficients are in use, depending on the electrical and mechanical boundary conditions imposed on the part under test. Each of the piezoelectric d, e, g, and h coefficients can be defined in terms of a direct and a converse effect the two sets of coefficients are related by thermodynamics. For example, the piezoelectric charge coefficient, dkjk, can be defined via [1] ... 

Mechanical properties are often overlooked when investigating piezoelectric polymers. It is important to note that the piezoelectric response is a result of the coupling between the mechanical and dielectric properties in an amorphous polymer. The piezoelectric coefficient, d, is defined as... 

Piezoelectric coefficient (d) The tensor that defines the coupling between external electric field under an applied stress is called the piezoelectric coefficient... 

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